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Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it.
This is the title page of the 1599 edition of the Rechenbuch of Simon Jacob (d. 1564), a Rechenmeister of the sixteenth century. This was a commercial arithmetic text, in which the basic laws of arithmetic were applied to many practical problems.
Mathematics is often referred to today as the "science of patterns." But has this always been true historically, or is this something that happened in recent times? The question is discussed here with reference to the work of Euclid and Jacob Steiner.
In baking a hemispherical loaf of bread of 10" radius, the crust was everywhere of an equal thickness, and the solidity of the crust was equal to half the solid content of the whole loaf. What were the dimensions of the interior soft part?
A horse, halving its speed each day, travels 700 miles in 7 days. How far does it travel each day?
Two bicyclists travel in opposite directions around a quarter-mile track and meet every 22 seconds. When they travel in the same direction on this track, the faster passes the slower once every 3 minutes and 40 seconds. Find the rate of each rider
Now there is a wall 5 feet thick and two rats tunnel from opposite sides.
Download the two winning essays to learn about using indivisibles to find the area under a cycloid arch in the 17th century and about the Radon transform and its use in x-ray tomography in the 20th century.
A four-sided town measures 1100 feet on one side and 1000 feet on the other side, on one edge 600 and the other edge 600.
This is the title page of Isaac Barrow's Latin edition of the works of Archimedes, the first four books of Apollonius's Conics, and Theodosius's Spherica. It was published in 1675.

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